What happens if you get too many rads in fallout new Vegas?

After 1000 rads you will die.

To prevent this use Rad-X in irradiated areas to lower the rads you get per second, and use Rad-Away if your radiation level goes to high, you can also seek out a doctor that can remove the radiation for you for 100-150 caps if you have high rad, and don't have any or enough Rad-Away.

there are also different perks that can increase your resistance to radiation.

...Desert Ranger 4...